Home
Class 12
MATHS
Prove that **: R xx R to R defined as a...

Prove that `**: R xx R to R ` defined as `a ** b =a+2ab` is not associative

Text Solution

Verified by Experts

`a ** (b**c)=a**(b+2c) AA a , b, c in R `
`= a+2(b+2c) =a+2b+4c`
and `(a**b)**c=(a+ 2b) ** c =a+2b+2c `
`:. a**(b**c) ne (a**b)**c`
`:. '**' ` is not associative .
Hence Proved .
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Exercies 1a|16 Videos

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Exercies 1b|18 Videos

  • PROBABIILITY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

Prove that **: R xx R to R defined as a ** b =a+2ab is not commutative .

Show that quad *:R xx R rarr R defined by a*b=a+2b is not commutative.

Show that *:R xx R rarr R given by a*b=a+2b is not associative.

Show that the relation R in R defined as R={(a,b):ageb} is transitive.

The binary operation *:R xx R rarr R is defined as a*b=2a+b* Find (2*3)*4

Examine whether the binary operation* defined on R by a*b=ab+1 is associative or not.

Prove that the relation R on Z defined by (a,b)in R hArr a-b is divisible by 5 is an equivalence relation on Z .

Let ^(*) be a binary operation on R defined by a*b=ab+1. Then,* is commutative but not associative associative but not commutative neither commutative nor associative (d) both commutative and associative

Prove that 2R cos A = 2R + r - r_(1)

NAGEEN PRAKASHAN-RELATIONS AND FUNCTIONS -Miscellaneous Exercise
  1. Prove that **: R xx R to R defined as a ** b =a+2ab is not associativ...

    Text Solution

    |

  2. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

    Text Solution

    |

  3. Let f: W ->Wbe defined as f(n) = n - 1, if is odd and f(n) = n + 1, i...

    Text Solution

    |

  4. If f: R ->Ris defined by f(x) = x^2- 3x + 2, find f(f(x)).

    Text Solution

    |

  5. Show that the function f: R rarr { x in R: -1 lt x lt 1 } defined by ...

    Text Solution

    |

  6. Show that the function f: R->Rgiven by f(x)=x^3is injective.

    Text Solution

    |

  7. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

    Text Solution

    |

  8. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

    Text Solution

    |

  9. Given a non-empty set X, consider P(X) which is the set of all subs...

    Text Solution

    |

  10. Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...

    Text Solution

    |

  11. Find the number of all onto functions from the set {1, 2, 3, , n)to ...

    Text Solution

    |

  12. Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...

    Text Solution

    |

  13. Consider the binary operations*: RxxR->R and o: RxxR->R defined as ...

    Text Solution

    |

  14. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

    Text Solution

    |

  15. Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod...

    Text Solution

    |

  16. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

    Text Solution

    |

  17. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

    Text Solution

    |

  18. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

    Text Solution

    |

  19. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

    Text Solution

    |

  20. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...

    Text Solution

    |